Journal ArticleDOI
Fuzzy systems as universal approximators
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An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy.Abstract:
An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown fuzzy patches from training data. These adaptive fuzzy systems approximate a function at two levels. At the local level the neural system approximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function. >read more
Citations
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Journal ArticleDOI
A variable selection method for a hierarchical interval type-2 TSK fuzzy inference system
TL;DR: A method to judge the degree of the relationship closeness between system input variables and theoretical output through independence test is proposed, and this method is applied to construct a hierarchical interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy inference system.
Proceedings ArticleDOI
Neuro-fuzzy controller for attitude-tracking stabilization of a multi-rotor unmanned aerial system
Jorge Cervantes,Filiberto Munoz,Ivan Gonzalez-Hernandez,Sergio Salazar,Isaac Chairez,Rogelio Lozano +5 more
TL;DR: In this paper, an automatic controller that solves the attitude stabilization for a quadrotor unmanned aerial system (UAS) was developed. But the controller used a simultaneous strategy of estimation and compensation of uncertainties as well as disturbances.
Proceedings ArticleDOI
Adaptive neuro-fuzzy identification method of Hammerstein model
TL;DR: In this article, the adaptive neuro-fuzzy identification for the Hammerstein model is investigated, which consists of the cascade structure of a static nonlinearity followed by a linear dynamic part.
Journal ArticleDOI
Statistical, connectionist, and fuzzy inference techniques for image classification
Steven A. Israel,Nikola Kasabov +1 more
TL;DR: A spectral classification comparison was performed using four different classifiers, the parametric maximum likelihood classifier and three nonparametric classifiers: neural networks, fuzzy rules, and fuzzy neural networks to classify mixed covertypes observed in an in situ field survey.
Journal ArticleDOI
Control of input delayed pneumatic vibration isolation table using adaptive fuzzy sliding mode
Amir Hd Markazi,Mostafa Khazaee +1 more
TL;DR: An adaptive fuzzy sliding mode controller is proposed to improve the performance of a pneumatic isolator in the low frequency range, i.e., where the passive techniques have obvious shortcomings, and the main advantage is that the closed-loop system stability is guaranteed under certain conditions.
References
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Journal ArticleDOI
Multilayer feedforward networks are universal approximators
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.
Journal ArticleDOI
Multilayer feedforward networks are universal approximators
HornikK.,StinchcombeM.,WhiteH. +2 more
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Journal ArticleDOI
Fuzzy basis functions, universal approximation, and orthogonal least-squares learning
Li-Xin Wang,Jerry M. Mendel +1 more
TL;DR: Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy.